I believe the arena would be more of a statium style area that would be for gladitorial style combat. If this is the case looting would be inapropriate. Realistically you could pick up a combatants weapon, but PS is a game first and vertual reality second. As it stands now. death does not seperate you from your armor, weapons and money so looting them from another players seems impossible to me.
I do not particuarly like this style of play. As much as I hated corpse runs in other games, I think they add to the fun of the game. I like things to be fair. If after I kill a monster I can pick apart its corpse, the same thing should be true for the monsters. I think the monsters should loot your corpse after you die just like you do to them. Consequently, If you loose a duel or are mugged, your mugger should be able to take all your items. I also would like to see realistic looting. You can not stuff 8 two handed swords in a backpack and then run back to town.
Unfortunatly, If I made a game like this, it would degenerate into a big mess, and no one would want to play it. PS is taking the proven path to making a role playing game. The key word being game. As a game it has restrictive rules that are there to improve the fun.
After saying all that, let me tell you that with computer AI as lame as it is now, player vs player combat is much more fun than Player vs computer ( or PvE as it is usually called).